The visitors to Dean Court held the Cherries at bay in the first half as the hosts missed a number of first half chances and took the lead shortly after the half an hour mark through Lucy Wood.
Bournemouth responded immediately through Katie James as the sides entered the break at 1-1, but Bedford started the second half quickly and retook the lead three minutes into the second half.
That goal from Melis Mehmet proved to be the winner as the Cherries were unable to break down a solid Bedford side despite throwing everything at them, and they were beaten.
Bournemouth now trail second-placed Plymouth by six points with one game in hand.
Jessica Hennessy and Jenna Markham (Image: Richard Crease)
They will need to win their remaining two games of the season against Lewes and Watford, wiping out an inferior goal difference of six in the process, and hope Bedford do them a favour on the final day against Argyle.
The Cherries exerted some good early pressure as they looked for a fast start to set them on their way.
Sophie Quirk was lively in the opening exchanges and was a threat down the left, but a couple of her early deliveries weren’t able to find a teammate.
Jenna Markham had a shot blocked in the box, before Quirk had an effort charged down after she got free in the centre of the area from a corner.
Bedford had a couple of early moments in attack and Katie Scadding had to be alert to tip a Sophie Byrom cross from the right onto the crossbar.
Jenna Markham (Image: Richard Crease)
The ever-threatening Quirk had another sight of goal but she shot over the bar after some good footwork, before Georgia Wilson fired towards goal after a neat move involving Quirk and Markham, but Meale saved comfortably.
Wilson headed over the bar from a Quirk cross and the latter player curled a shot wide not long afterwards.
Bedford survived a bit of a scramble as Meale saved a low Kenni Thompson effort and Kelci Bowers looked to cut it back to the arriving Markham, but the defence scrambled back to clear.
Scadding saved comfortably from an Abbie Bensted free kick and Bowers had a shot blocked on the edge of the box, before Bedford took the lead after 34 minutes.
Byrom got away from Freya Meadows Tuson on the Bedford left, her low cross evaded everyone but came through to Wood at the far post who had a simple finish to make it 1-0.
Katie James levelled for the Cherries (Image: Richard Crease)
Four minutes later, though, James scored her fourth goal at Dean Court to draw Bournemouth back level.
Thompson fired towards goal from the top of the box on the left and it was blocked out to the midfielder who charged onto it and powered it past Meale.
Quirk went close twice before the break, as she first shot just over the bar before a fantastic last-ditch block from the Bedford skipper Hannah Warren denied her when it looked certain she would score.
Wilson had a shot caught by Meale in first half stoppage time, as the teams entered the interval level.
The Cherries fell behind in the third minute of the second period.
Breon Grant crossed from the right, Scadding palmed it away but only as far as Mehmet, who turned home from the edge of the six-yard box.
Kelci Bowers (Image: Richard Crease)
Bournemouth were slow to get going in the second period but sought to up the ante and Meadows Tuson saw a shot blocked after a corner 12 minutes into the half.
Markham went close after an excellent bit of work to get past her marker on the right, she charged into the box before her effort on the angle went just the wrong side of the post.
A Cherries corner dropped threateningly in the six-yard box but no one could poke home, and Thompson shot off target when James teed up her up.
Boss Bleazard went to her bench with 25 minutes to play, as she introduced Zoe Barratt and Amber Treweek for Wilson and Meadows Tuson.
Sophie Quirk (Image: Richard Crease)
Shortly after coming on, Treweek delivered a dangerous cross that Quirk was not far away from touching home, but it went through to keeper Meale.
Bowers missed a good chance as she couldn’t quite adjust her body to apply the finishing touch to a Quirk cross, before Quirk fired wide at the near post.
Ellie Strippel and Phoebe Williams were brought on for James and Charlotte Harris, before Gemma McGuinness replaced Markham with eight minutes plus stoppage time to play.
Thompson shot just wide after a corner came out to her, before Meale denied McGuinness with a brilliant one-on-one save when a cross came to the winger at the far post.
The Cherries were unable to find a late equaliser despite late pressure and a couple of corners in the dying minutes and they were beaten.